We describe a new approach for developing and validating cognitive process models. We develop graphical models (specifically, hidden Markov models) both from human empirical data on a task, as well as from synthetic data traces generated by a cognitive process model of human behavior on the task. We show that considering differences between the two graphical models can unveil substantive and nuanced imperfections of cognitive process models that can then be addressed to increase (...) their fidelity to empirical data. (shrink)

Many different, seemingly mutually exclusive, theories of categorization have been proposed in recent years. The most notable theories have been those based on prototypes, exemplars, and causal models. This chapter provides “representation theorems” for each of these theories in the framework of probabilistic graphical models. More specifically, it shows for each of these psychological theories that the categorization judgments predicted and explained by the theory can be wholly captured using probabilistic graphical models. In (...) other words, probabilistic graphical models provide a lingua franca for these disparate categorization theories, and so we can quite directly compare the different types of theories. These formal results are used to explain a variety of surprising empirical results, and to propose several novel theories of categorization. (shrink)

Conditional independence tests have received special attention lately in machine learning and computational intelligence related literature as an important indicator of the relationship among the variables used by their models. In the field of probabilistic graphical models, which includes Bayesian network models, conditional independence tests are especially important for the task of learning the probabilistic graphical model structure from data. In this paper, we propose the full Bayesian significance test for tests of conditional (...) independence for discrete datasets. The full Bayesian significance test is a powerful Bayesian test for precise hypothesis, as an alternative to the frequentist’s significance tests (characterized by the calculation of the p-value). (shrink)

Probabilistic argumentation and neuro-argumentative systems offer new computational perspectives for the theory and applications of argumentation, but their principled construction involves two entangled problems. On the one hand, probabilistic argumentation aims at combining the quantitative uncertainty addressed by probability theory with the qualitative uncertainty of argumentation, but probabilistic dependences amongst arguments as well as learning are usually neglected. On the other hand, neuro-argumentative systems offer the opportunity to couple the computational advantages of learning and massive parallel computation (...) from neural networks with argumentative reasoning and explanatory abilities, but the relation of probabilistic argumentation frameworks with these systems has been ignored so far. Towards the construction of neuro-argumentative systems based on probabilistic argumentation, we associate a model of abstract argumentation and the graphical model of Boltzmann machines in order to (i... (shrink)

Effective recommendations on healthy food choice need to be personalized and sent out on a large scale. In this paper, we present a model of automatic message selection tailored on the characteristics of the recipient and focused on the reduction of red meat consumption. This model is obtained through the collaboration between social psychologists and artificial intelligence experts. Starting from selected psychosocial models on food choices and the framing effects of recommendation messages, we involved a sample of Italian participants (...) in an experiment in which they: filled out a first questionnaire, which was aimed at detecting the psychosocial antecedents of the intention to eat red/processed meat; read messages differing as to the framing of the hypothetical consequences of reducing versus not reducing red/processed meat consumption; filled out a second questionnaire, which was aimed at detecting participants’ reaction to the messages, as well as any changes in their intention to consume red/processed meat. Data collected were then employed to learn both the structure and the parameters of a Graphical Causal Model based on a Dynamic Bayesian Network, aimed to predicting the potential effects of message delivery from the observation of the psychosocial antecedents. Such probabilistic predictor is intended as the basis for developing automated interactions strategies using Deep Reinforcement Learning techniques. Discussion focuses on how to develop automatic interaction strategies able to foster mindful eating, thanks to considering the psychosocial characteristics of the people involved; sending messages tailored on these characteristics; adapting interaction strategies according to people’s reactions. (shrink)

While quantum theory cannot be described by a local hidden variable model, it is nevertheless possible to construct such models that exhibit features commonly associated with quantum mechanics. These models are also used to explore the question of \-ontic versus \-epistemic theories for quantum mechanics. Spekkens’ toy theory is one such model. It arises from classical probabilistic mechanics via a limit on the knowledge an observer may have about the state of a system. The toy theory for (...) the simplest possible underlying system closely resembles stabilizer quantum mechanics, a fragment of quantum theory which is efficiently classically simulable but also non-local. Further analysis of the similarities and differences between those two theories can thus yield new insights into what distinguishes quantum theory from classical theories, and \-ontic from \-epistemic theories. In this paper, we develop a graphical language for Spekkens’ toy theory. Graphical languages offer intuitive and rigorous formalisms for the analysis of quantum mechanics and similar theories. To compare quantum mechanics and a toy model, it is useful to have similar formalisms for both. We show that our language fully describes Spekkens’ toy theory and in particular, that it is complete: meaning any equality that can be derived using other formalisms can also be derived entirely graphically. Our language is inspired by a similar graphical language for quantum mechanics called the ZX-calculus. Thus Spekkens’ toy bit theory and stabilizer quantum mechanics can be analysed and compared using analogous graphical formalisms. (shrink)

Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

Learning the structure of event sequences is a ubiquitous problem in cognition and particularly in language. One possible solution is to learn a probabilistic generative model of sequences that allows making predictions about upcoming events. Though appealing from a neurobiological standpoint, this approach is typically not pursued in connectionist modeling. Here, we investigated a sequential version of the restricted Boltzmann machine, a stochastic recurrent neural network that extracts high-order structure from sensory data through unsupervised generative learning and can encode (...) contextual information in the form of internal, distributed representations. We assessed whether this type of network can extract the orthographic structure of English monosyllables by learning a generative model of the letter sequences forming a word training corpus. We show that the network learned an accurate probabilistic model of English graphotactics, which can be used to make predictions about the letter following a given context as well as to autonomously generate high-quality pseudowords. The model was compared to an extended version of simple recurrent networks, augmented with a stochastic process that allows autonomous generation of sequences, and to non-connectionist probabilistic models. We conclude that sequential RBMs and stochastic simple recurrent networks are promising candidates for modeling cognition in the temporal domain. (shrink)

Since the late nineties there has been an increased interested in probabilistic logic learning, an area within AI that combines machine learning with logic-based knowledge representation and uncertainty reasoning. Several different formalisms for combining first-order logic with probability reasoning have been proposed, and it has been studied how models in these formalisms can be automatically learned from data. -/- This talk starts with a brief introduction to probabilistic logic learning, after which we will focus on a relatively (...) new formalism known as CP-logic. CP-logic stands for “causal probabilistic logic”. It is a knowledge representation formalism that allows us to write down rules that indicate that a certain combination of conditions may cause certain effects with a particular probability (e.g., tossing a coin may cause a result of heads or tails, each with 50% probability). Besides the fact that this formalism is interesting for knowledge representation in itself, it also offers interesting opportunities from the machine learning point of view. Indeed, given the semantics of these CP-logic programs, learning them from data amounts to extracting probabilistic causal influences from data. We will discuss recent research on learning CP-logic programs, including: algorithms for learning them; how they relate to graphical models; and applications of learning CP-logic programs. (shrink)

Objects have dispositions. Dispositions are normally analyzed by providing a meaning to disposition ascriptions like ‘This piece of salt is soluble’. Philosophers like Carnap, Goodman, Quine, Lewis and many others have proposed analyses of such disposition ascriptions. In this paper we will argue with Quine that the proper analysis of ascriptions of the form ‘x is disposed to m ’, where ‘x’ denotes an object, ‘m’ a manifestation, and ‘C’ a condition, goes like this: ‘x is of natural kind k’, (...) and the generic ‘ks are m ’ is true. For the analysis of the generic, we propose an analysis in terms of causal powers: ‘ks have the causal power to m’. The latter, in turn, is analyzed in a very precise way, making use of Pearl’s probabilistic graphical causal models. We will show how this natural kind-analysis improves on standard conditional analyses of dispositions by avoiding the standard counterexamples, and that it gives rise to precise observable criteria under which the disposition ascription is true. (shrink)

Measures of algorithmic bias can be roughly classified into four categories, distinguished by the conditional probabilistic dependencies to which they are sensitive. First, measures of "procedural bias" diagnose bias when the score returned by an algorithm is probabilistically dependent on a sensitive class variable (e.g. race or sex). Second, measures of "outcome bias" capture probabilistic dependence between class variables and the outcome for each subject (e.g. parole granted or loan denied). Third, measures of "behavior-relative error bias" capture (...) class='Hi'>probabilistic dependence between class variables and the algorithmic score, conditional on target behaviors (e.g. recidivism or loan default). Fourth, measures of "score-relative error bias" capture probabilistic dependence between class variables and behavior, conditional on score. Several recent discussions have demonstrated a tradeoff between these different measures of algorithmic bias, and at least one recent paper has suggested conditions under which tradeoffs may be minimized. -/- In this paper we use the machinery of causal graphical models to show that, under standard assumptions, the underlying causal relations among variables forces some tradeoffs. We delineate a number of normative considerations that are encoded in different measures of bias, with reference to the philosophical literature on the wrongfulness of disparate treatment and disparate impact. While both kinds of error bias are nominally motivated by concern to avoid disparate impact, we argue that consideration of causal structures shows that these measures are better understood as complicated and unreliable measures of procedural biases (i.e. disparate treatment). Moreover, while procedural bias is indicative of disparate treatment, we show that the measure of procedural bias one ought to adopt is dependent on the account of the wrongfulness of disparate treatment one endorses. Finally, given that neither score-relative nor behavior-relative measures of error bias capture the relevant normative considerations, we suggest that error bias proper is best measured by score-based measures of accuracy, such as the Brier score. (shrink)

How can the forensic scientist rationally justify performing a sequence of tests and analyses in a particular case? When is it worth performing a test or analysis on an item? Currently, there is a large void in logical frameworks for making rational decisions in forensic science. The aim of this paper is to fill this void by presenting a step-by-step guide on how to apply Bayesian decision theory to routine decision problems encountered by forensic scientists on performing or not performing (...) a particular laboratory test or analysis. A decision-theoretic framework, composed of actions, states of nature, and utilities, models this problem, and an influence diagram translates its notions into a probabilistic graphical network. Within this framework, the expected value of information (EVOI) for the submission of an item to a particular test or analysis addresses the above questions. The development of a classical case example on whether to perform presumptive tests for blood before submitting the item for a DNA analysis illustrates the use of this model for source level questions in forensic biology (i.e., questions that ask whether a crime stain consisting of a particular body fluid comes from a particular person). We show how to construct an influence diagram for this example, and how sensitivity analyses lead to an optimal analytical sequence. The key idea is to show that such a Bayesian decisional approach provides a coherent framework for justifying the optimal analytical sequence for a particular case in forensic science. (shrink)

Cause and effect relationships play a central role in how we perceive and make sense of the world around us, how we act upon it, and ultimately, how we understand ourselves. Almost two decades ago, computer scientist Judea Pearl made a breakthrough in understanding causality by discovering and systematically studying the “Ladder of Causation” [Pearl and Mackenzie 2018], a framework that highlights the distinct roles of seeing, doing, and imagining. In honor of this landmark discovery, we name this the Pearl (...) Causal Hierarchy (PCH). In this chapter, we develop a novel and comprehensive treatment of the PCH through two complementary lenses, one logical-probabilistic and another inferential-graphical. Following Pearl’s own presentation of the hierarchy, we begin by showing how the PCH organically emerges from a well-specified collection of causal mechanisms (a structural causal model, or SCM). We then turn to the logical lens. Our first result, the Causal Hierarchy Theorem (CHT), demonstrates that the three layers of the hierarchy almost always separate in a measure theoretic sense. Roughly speaking, the CHT says that data at one layer virtually always underdetermines information at higher layers. Since in most practical settings the scientist does not have access to the precise form of the underlying causal mechanisms – only to data generated by them with respect to some of PCH’s layers – this motivates us to study inferences within the PCH through the graphical lens. Specifically, we explore a set of methods known as causal inference that enable inferences bridging PCH’s layers given a partial specification of the SCM. For instance, one may want to infer what would happen had an intervention been performed in the environment (second-layer statement) when only passive observations (first-layer data) are available. We introduce a family of graphical models that allows the scientist to represent such a partial specification of the SCM in a cognitively meaningful and parsimonious way. Finally, we investigate an inferential system known as docalculus, showing how it can be sufficient, and in many cases necessary, to allow inferences across PCH’s layers. We believe that connecting with the essential dimensions of human experience as delineated by the PCH is a critical step towards creating the next generation of AI systems that will be safe, robust, human-compatible, and aligned with the social good. (shrink)

Mechanist philosophers have examined several strategies scientists use for discovering causal mechanisms in neuroscience. Findings about the anatomical organization of the brain play a central role in several such strategies. Little attention has been paid, however, to the use of network analysis and causal modeling techniques for mechanism discovery. In particular, mechanist philosophers have not explored whether and how these strategies incorporate information about the anatomical organization of the brain. This paper clarifies these issues in the light of the distinction (...) between structural, functional and effective connectivity. Specifically, we examine two quantitative strategies currently used for causal discovery from functional neuroimaging data: dynamic causal modeling and probabilistic graphical modeling. We show that dynamic causal modeling uses findings about the brain’s anatomical organization to improve the statistical estimation of parameters in an already specified causal model of the target brain mechanism. Probabilistic graphical modeling, in contrast, makes no appeal to the brain’s anatomical organization, but lays bare the conditions under which correlational data suffice to license reliable inferences about the causal organization of a target brain mechanism. The question of whether findings about the anatomical organization of the brain can and should constrain the inference of causal networks remains open, but we show how the tools supplied by graphical modeling methods help to address it. (shrink)

Questions concerning mediated causal effects are of great interest in psychology, cognitive science, medicine, social science, public health, and many other disciplines. For instance, about 60% of recent papers published in leading journals in social psychology contain at least one mediation test (Rucker, Preacher, Tormala, & Petty, 2011). Standard parametric approaches to mediation analysis employ regression models, and either the “difference method” (Judd & Kenny, 1981), more common in epidemiology, or the “product method” (Baron & Kenny, 1986), more common (...) in the social sciences. In this article, we first discuss a known, but perhaps often unappreciated, fact that these parametric approaches are a special case of a general counterfactual framework for reasoning about causality first described by Neyman (1923) and Rubin (1924) and linked to causal graphical models by Robins (1986) and Pearl (2006). We then show a number of advantages of this framework. First, it makes the strong assumptions underlying mediation analysis explicit. Second, it avoids a number of problems present in the product and difference methods, such as biased estimates of effects in certain cases. Finally, we show the generality of this framework by proving a novel result which allows mediation analysis to be applied to longitudinal settings with unobserved confounders. (shrink)

Exploratory analyses are an important first step in psychological research, particularly in problem-based research where various variables are often included from multiple theoretical perspectives not studied together in combination before. Notably, exploratory analyses aim to give first insights into how items and variables included in a study relate to each other. Typically, exploratory analyses involve computing bivariate correlations between items and variables and presenting them in a table. While this is suitable for relatively small data sets, such tables can easily (...) become overwhelming when datasets contain a broad set of variables from multiple theories. We propose the Gaussian graphical model as a novel exploratory analyses tool and present a systematic roadmap to apply this model to explore relationships between items and variables in environmental psychology research. We demonstrate the use and value of the Gaussian graphical model to study relationships between a broad set of items and variables that are expected to explain the effectiveness of community energy initiatives in promoting sustainable energy behaviors. (shrink)

The past century has witnessed numerous methodological innovations in probabilistic and statistical methods of causal inference (e.g., the graphical modelling and the potential outcomes frameworks, as introduced in Chapter 1). These innovations have not only enhanced the methodologies by which scientists across diverse domains make causal inference, but they have also made a profound impact on the way philosophers think about causation. The philosophical issues discussed in this thesis are stimulated and inspired by these methodological innovations. Chapter 2 (...) addresses the question of how the holding of screening-off conditions for a causal model depends on the choice of variables. As bridge principles between probability and causation, screening-off conditions (especially the Causal Markov Condition) play a key role in causal inference. However, it has been known that these conditions may fail due to poor variable choice. My aim in this chapter is to further examine those constraints on variable choice that are deemed necessary for the satisfaction of screening-off conditions. The idea of a well-defined (hypothetical) intervention is also crucial for reliable causal inference. Chapter 3 explores the question of when interventions invoked in causal inference are “well-defined” or unambiguous, and how this requirement constrains the choice of cause-variables. I propose that an intervention is well-defined just in case the effect of interest is well-defined (under ideal interventions), and that the intervention can serve as a suitable means to identify that effect. Based on this proposal, several distinct types of ambiguous interventions are identified. Methodological progress in causal inference also poses the following question: Can such progress shed light on the ontology of causation? My answer is yes. In Chapter 4, I develop a Carnapian-pragmatist approach to the ontology of causation as an alternative to existing metaphysical approaches. I argue that, compared to traditional metaphysics, the pragmatist approach provides a superior picture of how the ontology and methodology of causation interact with each other in scientific practice. I conclude in Chapter 5 that the thing we call “causation” consists in both the right worldly infrastructure (e.g., screening-off patterns and possibilities for interventions) and appropriate ways of framing this infrastructure. (shrink)

The aim of the paper is to develop the notion of partial probability distributions as being more realistic models of belief systems than the standard accounts. We formulate the theory of partial probability functions independently of any classical semantic notions. We use the partial probability distributions to develop a formal semantics for partial propositional calculi, with extensions to predicate logic and higher order languages. We give a proof theory for the partial logics and obtain soundness and completeness results.

A graphical model is a graph that represents a set of conditional independence relations among the vertices (random variables). The graph is often given a causal interpretation as well. I describe how graphical causal models can be used in an algorithm for constructing partial information about causal graphs from observational data that is reliable in the large sample limit, even when some of the variables in the causal graph are unmeasured. I also describe an algorithm for estimating (...) from observational data (in some cases) the total effect of a given variable on a second variable, and theoretical insights into fundamental limitations on the possibility of certain causal inferences by any algorithm whatsoever, and regardless of sample size. (shrink)

Words are the essence of communication: They are the building blocks of any language. Learning the meaning of words is thus one of the most important aspects of language acquisition: Children must first learn words before they can combine them into complex utterances. Many theories have been developed to explain the impressive efficiency of young children in acquiring the vocabulary of their language, as well as the developmental patterns observed in the course of lexical acquisition. A major source of disagreement (...) among the different theories is whether children are equipped with special mechanisms and biases for word learning, or their general cognitive abilities are adequate for the task. We present a novel computational model of early word learning to shed light on the mechanisms that might be at work in this process. The model learns word meanings as probabilistic associations between words and semantic elements, using an incremental and probabilistic learning mechanism, and drawing only on general cognitive abilities. The results presented here demonstrate that much about word meanings can be learned from naturally occurring child-directed utterances (paired with meaning representations), without using any special biases or constraints, and without any explicit developmental changes in the underlying learning mechanism. Furthermore, our model provides explanations for the occasionally contradictory child experimental data, and offers predictions for the behavior of young word learners in novel situations. (shrink)

Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One prominent approach to tackling this problem is based on causal Bayesian networks, using directed acyclic graphs as causal diagrams to relate post-intervention probabilities to pre-intervention probabilities that are estimable from observational data. However, such causal diagrams are (...) seldom fully testable given observational data. In consequence, many causal discovery algorithms based on data-mining can only output an equivalence class of causal diagrams. This paper is concerned with causal reasoning given an equivalence class of causal diagrams, represented by a ancestral graph. We present two main results. The first result extends Pearl 's celebrated do-calculus to the context of ancestral graphs. In the second result, we focus on a key component of Pearl's calculus---the property of invariance under interventions, and give stronger graphical conditions for this property than those implied by the first result. The second result also improves the earlier, similar results due to Spirtes et al. (shrink)

We propose a new approach for tracing value change. Value change may lead to a mismatch between current value priorities in society and the values for which technologies were designed in the past, such as energy technologies based on fossil fuels, which were developed when sustainability was not considered a very important value. Better anticipating value change is essential to avoid a lack of social acceptance and moral acceptability of technologies. While value change can be studied historically and qualitatively, we (...) propose a more quantitative approach that uses large text corpora. It uses probabilistic topic models, which allow us to trace values that are latent. We demonstrate the approach for five types of value change in technology. Our approach is useful for testing hypotheses about value change, such as verifying whether value change has occurred and identifying patterns of value change. The approach can be used to trace value change for various technologies and text corpora, including scientific articles, newspaper articles, and policy documents. (shrink)

JiJi Zhang and Peter Spirtes. A Characterization of Markov Equivalence Classes for Ancestral Graphical Models.

In everyday life, as well as in science, we have to deal with and act on the basis of partial (i.e. incomplete, uncertain, or even inconsistent) information. This observation is the source of a broad research activity from which a number of competing approaches have arisen. There is some disagreement concerning the way in which partial or full ignorance is and should be handled. The most successful approaches include both quantitative aspects (by means of probability theory) and qualitative aspect (by (...) means of graphical or causal models or logic). Some of these approaches have important impacts on various disciplines including philosophy, computer science, statistics, mathematics, physics, and social science. Most notably, the relation between causal and probabilistic information is a topic of interest in all of these fields. (shrink)

Background: Empirical ethics inquiry works from the notion that stakeholder perspectives are necessary for gauging the ethical acceptability of human studies and assuring that research aligns with societal expectations. Although common, studies involving different populations often entail comparisons of trends that problematize the interpretation of results. Using graphical model selection—a technique aimed at transcending limitations of conventional methods—this report presents data on the ethics of clinical research with two objectives: (1) to display the patterns of views held by ill (...) and healthy individuals in clinical research as a test of the study's original hypothesis and (2) to introduce graphical model selection as a key analytic tool for ethics research. Methods: In this institutional review board (IRB)-approved, National Institutes of Health-funded project, data were collected from 60 mentally ill and 43 physically ill clinical research protocol volunteers, 47 healthy protocol-consented participants, and 29 healthy individuals without research protocol experience. Respondents were queried on the ethical acceptability of research involving people with mental and physical illness (i.e., cancer, HIV, depression, schizophrenia, and posttraumatic stress disorder) and non-illness-related sources of vulnerability (e.g., age, class, gender, ethnicity). Using a statistical algorithm, we selected graphical models to display interrelationships among responses to questions. Results: Both mentally and physically ill protocol volunteers revealed a high degree of connectivity among ethically salient perspectives. Healthy participants, irrespective of research protocol experience, revealed patterns of views that were not highly connected. Conclusions: Between ill and healthy protocol participants, the pattern of views was vastly different. Experience with illness was tied to dense connectivity, whereas healthy individuals expressed views with sparse connections. In offering a nuanced perspective on the interrelation of ethically relevant responses, graphical model selection has the potential to bring new insights to the field of ethics. (shrink)

Understanding and solving the psychological health problems of college students have become a focus of social attention. Complex networks have become important tools to study the factors affecting psychological health, and the Gaussian graphical model is often used to estimate psychological networks. However, previous studies leave some gaps to overcome, including the following aspects. When studying networks of subpopulations, the estimation neglects the intrinsic relationships among subpopulations, leading to a large difference between the estimated network and the real network. (...) Because of the high cost, previous psychological surveys often have a small sample size, and the psychological description is insufficient. Here, the intrinsic connections among multiple tasks are used, and multitask machine learning is applied to develop a multitask Gaussian graphical model. The psychological networks of the population and subpopulations are estimated based on psychological questionnaire data. This study is the first to apply a psychological network to such a large-scale college student psychological analysis, and we obtain some interesting results. The model presented here is a dynamic model based on complex networks which predicts individual behavior and provides insight into the intrinsic links among various symptoms. (shrink)

A key challenge for probabilistic causal models is to distinguish non-causal probabilistic dependencies from true causal relations. To accomplish this task, causal models are usually required to satisfy several constraints. Two prominent constraints are the causal Markov condition and the faithfulness condition. However, other constraints are also needed. One of these additional constraints is the causal sufficiency condition, which states that models must not omit any direct common causes of the variables they contain. In this (...) paper, I argue that the causal sufficiency condition is problematic: (1) it is incompatible with the requirement that the variables in a model must not stand in non-causal necessary dependence relations, such as mathematical or conceptual relations, or relations described in terms of supervenience or grounding, (2) it presupposes more causal knowledge as primitive than is actually needed to create adequate causal models, and (3) if models are only required to be causally sufficient, they cannot deal with cases where variables are probabilistically related by accident, such as Sober’s example of the relationship between bread prices in England and the sea level in Venice. I show that these problems can be avoided if causal models are required to be monotonic in the following sense: the causal relations occurring in a model M would not disappear if further variables were added to M. I give a definition of this monotonicity condition and conclude that causal models should be required to be monotonic rather than causally sufficient. (shrink)

Peter Spirtes. Conditional Independence in Directed Cyclical Graphical Models Representing Feedback or Mixtures.

Peter Spirtes. Conditional Independence in Directed Cyclic Graphical Models for Feedback.

In this article, we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model with given observational data. We build on an algorithm proposed by Wang and Drton, and we show that one can augment the hidden variable structure of the recovered model by learning multidirected edges rather than only directed and bidirected ones. Multidirected edges appear when more than two of the observed variables have a hidden common cause. We detect the (...) presence of such hidden causes by looking at higher order cumulants and exploiting the multi-trek rule. Our method recovers the correct structure when the underlying graph is a bow-free acyclic mixed graph with potential multidirected edges. (shrink)

This paper presents a proof of concept for a graphical models approach to assessing the moral coherence and moral robustness of systems of social interactions. “Moral coherence” refers to the degree to which the rights and duties of agents within a system are effectively respected when agents in the system comply with the rights and duties that are recognized as in force for the relevant context of interaction. “Moral robustness” refers to the degree to which a system of (...) social interaction is configured to ensure that the interests of agents are effectively respected even in the face of noncompliance. Using the case of conscientious objection of pharmacists to filling prescriptions for emergency contraception as an example, we illustrate how a graphical models approach can help stakeholders identify structural weaknesses in systems of social interaction and evaluate the relative merits of alternate organizational structures. By illustrating the merits of a graphical models approach we hope to spur further developments in this area. (shrink)

Peter Spirtes. Discovering Causal Relations Among Latent Variables in Directed Acyclical Graphical Models.

We study the selection of adjustment sets for estimating the interventional mean under an individualized treatment rule. We assume a non-parametric causal graphical model with, possibly, hidden variables and at least one adjustment set composed of observable variables. Moreover, we assume that observable variables have positive costs associated with them. We define the cost of an observable adjustment set as the sum of the costs of the variables that comprise it. We show that in this setting there exist adjustment (...) sets that are minimum cost optimal, in the sense that they yield non-parametric estimators of the interventional mean with the smallest asymptotic variance among those that control for observable adjustment sets that have minimum cost. Our results are based on the construction of a special flow network associated with the original causal graph. We show that a minimum cost optimal adjustment set can be found by computing a maximum flow on the network, and then finding the set of vertices that are reachable from the source by augmenting paths. The optimaladj Python package implements the algorithms introduced in this article. (shrink)